3.1152 \(\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^3} \, dx\)

Optimal. Leaf size=38 \[ -\frac{50 x}{27}+\frac{8}{9 (3 x+2)}-\frac{7}{162 (3 x+2)^2}+\frac{65}{27} \log (3 x+2) \]

[Out]

(-50*x)/27 - 7/(162*(2 + 3*x)^2) + 8/(9*(2 + 3*x)) + (65*Log[2 + 3*x])/27

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Rubi [A]  time = 0.0472973, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{50 x}{27}+\frac{8}{9 (3 x+2)}-\frac{7}{162 (3 x+2)^2}+\frac{65}{27} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3,x]

[Out]

(-50*x)/27 - 7/(162*(2 + 3*x)^2) + 8/(9*(2 + 3*x)) + (65*Log[2 + 3*x])/27

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{65 \log{\left (3 x + 2 \right )}}{27} + \int \left (- \frac{50}{27}\right )\, dx + \frac{8}{9 \left (3 x + 2\right )} - \frac{7}{162 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(3+5*x)**2/(2+3*x)**3,x)

[Out]

65*log(3*x + 2)/27 + Integral(-50/27, x) + 8/(9*(3*x + 2)) - 7/(162*(3*x + 2)**2
)

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Mathematica [A]  time = 0.0399809, size = 35, normalized size = 0.92 \[ \frac{1}{162} \left (-\frac{3 \left (600 x^2+656 x+173\right )}{(3 x+2)^2}-300 x+390 \log (3 x+2)\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3,x]

[Out]

(-300*x - (3*(173 + 656*x + 600*x^2))/(2 + 3*x)^2 + 390*Log[2 + 3*x])/162

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Maple [A]  time = 0.01, size = 31, normalized size = 0.8 \[ -{\frac{50\,x}{27}}-{\frac{7}{162\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{8}{18+27\,x}}+{\frac{65\,\ln \left ( 2+3\,x \right ) }{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)^2/(2+3*x)^3,x)

[Out]

-50/27*x-7/162/(2+3*x)^2+8/9/(2+3*x)+65/27*ln(2+3*x)

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Maxima [A]  time = 1.35073, size = 42, normalized size = 1.11 \[ -\frac{50}{27} \, x + \frac{432 \, x + 281}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{65}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^3,x, algorithm="maxima")

[Out]

-50/27*x + 1/162*(432*x + 281)/(9*x^2 + 12*x + 4) + 65/27*log(3*x + 2)

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Fricas [A]  time = 0.215496, size = 63, normalized size = 1.66 \[ -\frac{2700 \, x^{3} + 3600 \, x^{2} - 390 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 768 \, x - 281}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^3,x, algorithm="fricas")

[Out]

-1/162*(2700*x^3 + 3600*x^2 - 390*(9*x^2 + 12*x + 4)*log(3*x + 2) + 768*x - 281)
/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.276518, size = 29, normalized size = 0.76 \[ - \frac{50 x}{27} + \frac{432 x + 281}{1458 x^{2} + 1944 x + 648} + \frac{65 \log{\left (3 x + 2 \right )}}{27} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)**2/(2+3*x)**3,x)

[Out]

-50*x/27 + (432*x + 281)/(1458*x**2 + 1944*x + 648) + 65*log(3*x + 2)/27

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GIAC/XCAS [A]  time = 0.209357, size = 36, normalized size = 0.95 \[ -\frac{50}{27} \, x + \frac{432 \, x + 281}{162 \,{\left (3 \, x + 2\right )}^{2}} + \frac{65}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^3,x, algorithm="giac")

[Out]

-50/27*x + 1/162*(432*x + 281)/(3*x + 2)^2 + 65/27*ln(abs(3*x + 2))